A Theory of Rolling Horizon Decision Making
Annals of Operations Research, Vol. 29, No. 1, December 1991
29 Pages Posted: 30 Jan 2008 Last revised: 7 May 2014
Abstract
In this paper, we develop a theoretical framework for the common business practice of rolling horizon decision making. The main idea of our approach is that the usefulness of rolling horizon methods is, to a great extent, implied by the fact that forecasting the future is a costly activity. We, therefore, consider a general, discrete-time, stochastic dynamic optimization problem in which the decision maker has the possibility to obtain information on the uncertain future at given cost. For this non-standard optimization problem with optimal stopping decisions, we develop a dynamic programming formulation. We treat both finite and infinite horizon cases. We also provide a careful interpretation of the dynamic programming equations and illustrate our results by a simple numerical example. Various generalizations are shown to be captured by straightforward modifications of our model.
Keywords: rolling horizon, stochastic dynamic optimization, dynamic programming, forecast horizons, decision horizons, planning horizons, forecasting
JEL Classification: C61, M10
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